Numerical methods for a model for compressible miscible displacement in porous media.

*(English)*Zbl 0537.76062The authors derive a nonlinear parabolic system for single-phase, miscible displacement of one compressible fluid by another in a porous medium under the assumption that no volume change results from the mixing of the components and that a pressure-density relation exists for each component in a form that is independent of mixing implying that fluids are in the liquid state. They analyse two numerical schemes for approximating the solution of a two component system only for concentration of fluid and pressure using a parabolic Galerkin procedure for the concentration equation for both the schemes but a parabolic Galerkin procedure for the first scheme and a parabolic mixed finite element technique for the second numerical scheme for the pressure equation.

It is claimed that the two procedures used for the two-component model can easily be generalized to treat an n-component model. The formulations and analysis are new and are of great interest to people working in ’numerical analysis’ and ’petroleum engineering’. [This is an abridged version, the complete review is available on demand.]

It is claimed that the two procedures used for the two-component model can easily be generalized to treat an n-component model. The formulations and analysis are new and are of great interest to people working in ’numerical analysis’ and ’petroleum engineering’. [This is an abridged version, the complete review is available on demand.]

Reviewer: H.K.Verma

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76T99 | Multiphase and multicomponent flows |

76M99 | Basic methods in fluid mechanics |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |